As much as any policy tensions or messaging debate within the party, this question of tone — of how to combat Mr. Trump effectively without slipping into a pale imitation — is perhaps the central divide of this Democratic moment (and the next one, with the 2020 campaign looming).

How will Democrats choose to revise Mrs. Obama’s sentence, with Mr. Trump heaving insults from the White House and the rally stage — his pre-midterm bully pulpit?

“When they go low, we kick them,” Eric H. Holder Jr., the former Obama administration attorney general and a possible 2020 candidate, said this week.

“When they go low, I say hit back harder,” Michael Avenatti, the cable-ubiquitous lawyer flirting with his own presidential run as a Trump-style brawler, told a crowd in Iowa over the summer.

Few but Mrs. Obama seemed inclined to defend the original refrain. “Fear,” Mrs. Obama told NBC on Thursday, “is not a proper motivator. Hope wins out.”

But for many Democrats, it does not seem to be winning out, at least for now.

It is one thing for Mr. Avenatti, the party’s telegenic anti-Trump id, to seize this kind of rhetorical real estate. But increasingly, much of the Democratic establishment seems to be marching that way, too, channeling the righteous anger of the progressive base.

Going high, these Democrats say, got them a Trump administration and minority status in Congress. Going high got them a Supreme Court justice accused of sexual assault, nominated by a president accused of sexual assault (both deny it).

“You cannot be civil with a political party that wants to destroy what you stand for,” Hillary Clinton told CNN this week. “If we are fortunate enough to win back the House and/or the Senate, that’s when civility can start again. But until then, the only thing that the Republicans seem to recognize and respect is strength.”

Mrs. Clinton seems unlikely to recommend her 2016 campaign slogan, “Stronger Together,” to the next generation. Yet if she failed to reflect the national mood during her last run, Democrats had spent years before that straining to project indignation in the right proportions.

Former President Barack Obama could seem removed, ever mindful of the minefields underfoot for a black politician emitting fury.

Mrs. Clinton, before her 2016 turn as a stateswoman and grandmother, staked her 2008 bid on evincing a toughness that could match any man’s.

Former Vice President Joseph R. Biden Jr. has held himself out as a Democratic rarity: unwilling to give up on the white working-class voters who lifted Mr. Trump, but unafraid to go nose to nose with their president.

The result: down-home paeans to a well-placed whupping.

“If we were in high school,” Mr. Biden said earlier this year, “I’d take him behind the gym and beat the hell out of him.”

While the wisdom of such confrontation in a national race remains untested, this year’s Democratic primary season demonstrated that many voters are prepared to reward more insurgent energy in the party. Upsets from movement-minded progressives like Ayanna Pressley in Massachusetts and Alexandria Ocasio-Cortez in New York were powered, in large measure, by impatience with incumbents who lacked what Ms. Pressley called “activist leadership,” even if they generally voted as liberals wanted.

At the same time, many Democrats have cautioned against embracing anger as an organizing principle, suggesting that harnessing disdain for Mr. Trump is workable only if voters also broadly understand what the party stands for.

“Rage is good. Rage fuels people to step up and pay attention,” said Amanda Litman, a former campaign aide to Mrs. Clinton who now oversees Run for Something, a group dedicated to recruiting first-time candidates. “That being said, it isn’t necessarily sustainable. It’s hard to be angry for two years.”

She reconsidered after a moment. “Or at least it’s hard to be productively angry,” Ms. Litman said. “I’ve been angry for two years.”

Mitch McConnell, the Senate majority leader, quoted both Mrs. Clinton and Mr. Holder from the Senate floor on Thursday, adding, “We will not let mob behavior drown out all the Americans who want to legitimately participate in the policymaking process.”

Later on Thursday, Mr. Holder tweeted a clarification that many Democrats did not think was necessary: He was not literally telling supporters to kick Republicans, as his full remarks made clear.

“I’m saying Republicans are undermining our democracy,” he wrote, “and Democrats need to be tough, proud and stand up for the values we believe in.”

(Mr. Holder was not to be confused with Mr. Avenatti, who had in fact proposed a three-round mixed martial arts fight with Donald Trump Jr. for charity.)

For other prospective 2020 challengers, the last few months have been a field test of sorts for how to navigate the new world.

Senator Cory Booker of New Jersey has balanced a “lead with love” playbook for engaging political opponents with a forceful, front-facing role on the Senate Judiciary Committee during the Kavanaugh confirmation, when Democrats sought to sink his nomination.

Senator Elizabeth Warren of Massachusetts — among the most assertive Democrats in responding to Mr. Trump on his favored social medium — specks her speeches with the word “fight” so often that it can feel like subliminal messaging. The title of her book last year: “This Fight Is Our Fight.”

During the midterms, candidate zeal has often been dictated largely by zip code.

“It depends on where Republicans are going low,” said Steve Israel, a former New York congressman and chairman of the Democratic Congressional Campaign Committee. “If they’re going low in North Dakota, you offer to build a bridge to bring them back. If they’re going low in Brooklyn, New York, you hit them on the head with a two-by-four.”

In the Senate’s most high-profile race this year — between Senator Ted Cruz of Texas and Representative Beto O’Rourke — Mr. O’Rourke has tested the limits of this strategy, preaching high-mindedness and understanding in deep-red corners of Texas and declining to moderate his liberal politics.

The approach has earned him tens of millions of dollars in donations and viral celebrity in the party — his stylistic contrast to Mr. Cruz laid bare in a debate-night exchange last month.

The candidates had been asked to say a kind word about each other. Mr. O’Rourke cited Mr. Cruz’s sacrifice as a public official working away from his family. Mr. Cruz saluted what he called Mr. Rourke’s sincere belief in wrongheaded positions like “expanding government and higher taxes.”